System Of Nonhomogeneous Equations Research Articles

Effect of spin fluctuations on the superconducting phase of Hubbard fermions in the t-t′-t″-J* model

The effect of spin-fluctuation scattering processes on the region of the superconducting phase in strongly correlated electrons (Hubbard fermions) is investigated by the diagram technique for Hubbard operators. Modified Gor’kov equations in the form of an infinitely large system of integral equations are derived taking into account contributions of anomalous components \( P_{0\sigma ,\bar \sigma 0} \) of strength operator \( \hat P \). It is shown that spinfluctuation scattering processes in the one-loop approximation for the t-t′-t″-J* model taking into account long-range hoppings and three-center interactions are reflected by normal (P0σ, 0σ) and anomalous (\( P_{0\sigma ,\bar \sigma 0} \)) components of the strength operator. Three-center interactions result in different renormalizations of the kernels of the integral equations for the superconducting d phase in the expressions for the self-energy and strength operators. In this approximation for the d-type symmetry of the order parameter for the superconducting phase, the system of integral equations is reduced to a system of nonhomogeneous equations for amplitudes. The resultant dependences of critical temperature on the electron concentrations show that joint effect of long-range hoppings, three-center interactions, and spin-fluctuation processes leads to strong renormalization of the superconducting phase region.

A spiral model for bending of non-linearly pretwisted helicoidal structures with lateral loading

The paper presents a new approach in the bending analysis of helicoidal structures with a large non-linear pretwist and an external lateral loading. It also addresses the issue as to what extent the linearized twisting curvature is applicable in the analysis of pretwisted plates. Employing a non-linear helicoidal model and a natural orthogonal coordinate system, the large non-linear pretwist is formulated and the energy stored in a distorted helicoid subjected to an external pressure normal to the helicoid axis is derived. By integrating the internal strain energy and external pressure work over the helicoidal domain, a non-homogeneous system of equations is presented and numerical solutions are obtained. Significant structural responses such as deformation components and resultant, the effects of width and thickness of helicoid on bending are analyzed and discussed. The analysis can be extended to other areas of interest such as turbomachinery blades, drilling structures, motors in micro-electro-mechanical systems and also DNA biomechanics.

VIBRATIONS OF FRONT SUSPENSION OF A CAR

SUMMARY In this work the vibratory behaviour of the front suspension of a car is investigated. In the system of the suspension a pneumatic tyre is also included, as a vibroactive element in the considered frequency range 50–200 Hz. A plane mathematical model of the considered system has been made, which is described by differential equations. An account has been given of the influence of the elastic and damping properties of the rubber vibroisolators, the elastic properties of the links and the geometry of the suspension. In a unity the behaviour of the separate elements as solid bodies and such with distributed masses is studied. A periodic disturbing power in the contact area between the tyre and the road is included. By making the system of the differential equations linear a system of non-homogeneous equations is obtained.

General Field Theory Treatment of H-Plane Waveguide Junction Circulators

In this paper an exact field theory treatment for the waveguide junction circulators is presented. The treatment is general, being dependent on neither the geometrical symmetry of the junction nor the number of ports. The electromagnetic fields in the joining waveguides are written in the form of infinite summation of waveguide modes. The solutions of the wave equations in the ferrite rod and in the surrounding air are obtained in the form of infinite summation of cylindrical modes. The fields at the ferrite air interface and at an imaginary boundary chosen arbitrarily between the air region and the waveguides are then matched. This process leads to an infinite system of nonhomogeneous equations in the field amplitudes. Three types of waveguide junction circulators using this technique are analyzed: the simple ferrite-rod Y junction, the simple ferrite-rod T junction, and the latching Y junction. Point-matching techniques are used to get numerical results for the field distributions and the circulator characteristics. Excellent agreement has been found between the published experimental measurements and the numerical results obtained by this technique.